EP 2 570 351 A1 discloses a thermoform packaging machine with a forming station for forming packages with an undercut. Thermoform packaging machines that form packages with a very small undercut use a clamp chain provided on both sides of the film for transporting the film and holding the formed film when the forming tool lower part is being opened. The tensile forces due to the undercut acting on the formed film during opening of the forming tool lower part can be taken up by the clamp chains only to a limited extent and the film will be pulled out of the clamp chains when the tensile forces are too large.